Regularity of the Hardy-Littlewood maximal operator on block decreasing functions

We study the Hardy-Littlewood maximal operator defined via an unconditional norm, acting on block decreasing functions. We show that the uncentered maximal operator maps block decreasing functions of special bounded variation to functions with integrable distributional derivatives, thus improving their regularity. In the special case of the maximal operator defined by the l_infty-norm, that is, by averaging over cubes, the result extends to block decreasing functions of bounded variation, not necessarily special.Comment: 26 page

Dynamics and bifurcations in a simple quasispecies model of tumorigenesis

Cancer is a complex disease and thus is complicated to model. However, simple models that describe the main processes involved in tumoral dynamics, e.g., competition and mutation, can give us clues about cancer behaviour, at least qualitatively, also allowing us to make predictions. Here we analyze a simplified quasispecies mathematical model given by differential equations describing the time behaviour of tumor cells populations with different levels of genomic instability. We find the equilibrium points, also characterizing their stability and bifurcations focusing on replication and mutation rates. We identify a transcritical bifurcation at increasing mutation rates of the tumor cells population. Such a bifurcation involves an scenario with dominance of healthy cells and impairment of tumor populations. Finally, we characterize the transient times for this scenario, showing that a slight increase beyond the critical mutation rate may be enough to have a fast response towards the desired state (i.e., low tumor populations) during directed mutagenic therapies

Management system requirements for wireless systems beyond 3G

This paper presents a comprehensive description of various management system requirements for systems beyond 3G, which have been identified as a result of the Software Based Systems activities within the Mobile VCE Core 2 program. Specific requirements for systems beyond 3G are discussed and potential technologies to address them proposed. The analysis has been carried out from network, service and security viewpoints

Backscatter Transponder Based on Frequency Selective Surface for FMCW Radar Applications

This paper describes an actively-controlled frequency selective surface (FSS) to implement a backscatter transponder. The FSS is composed by dipoles loaded with switching PIN diodes. The transponder exploits the change in the radar cross section (RCS) of the FSS with the bias of the diodes to modulate the backscattered response of the tag to the FMCW radar. The basic operation theory of the system is explained here. An experimental setup based on a commercial X-band FMCW radar working as a reader is proposed to measure the transponders. The transponder response can be distinguished from the interference of non-modulated clutter, modulating the transponder’s RCS. Some FSS with different number of dipoles are studied, as a proof of concept. Experimental results at several distances are provided

Upscaling mixing-limited chemical reactions from pore to continuum scale using the dispersive lamella concept

Reactive transport modeling is an important tool for the analysis of coupled physical, chemical, and biological processes in Earth systems. Observed reactive transport in heterogeneous porous media shows a different behavior than the established transport laws for homogeneous media. Natural aquifers exhibit physical and chemical heterogeneities at all scales, which leads to reaction and transport dynamics that cannot be explained by traditional reactive models based on the advection-dispersion-reaction equation (ADRE). In particular, the discrepancy is traced back to the nonuniform nature of flow velocity fields, complex spatial concentration distributions, and the degree of mixing between reactants. The role and contribution of these factors is key to provide accurate predictions of reactions. The complexity of the task lies in the enormous range of spatial and temporal scales that reactants find in natural porous media. Hence, the complete characterization of the fate of chemical reactions requires that models accounts for the basic mechanisms that govern the mixing and reaction dynamics. In this thesis, we present a novel methodology for the simulation of homogeneous chemical reactions. The proposed methodology is a random walk particle tracking approach (RWPT) coupled with reactions that simulates bimolecular chemical reactions, and is equivalent to the ADRE. Reactions among particles are determined by a reaction probability given in terms of the reaction rate coefficient, the total number of particles, and an interaction radius that describes a well-mixed support volume at which all particles have the same probability to react. The method is meshless and free of numerical dispersion. The RWPT approach is validated against analytical solutions for different flow scenarios under slow and fast reaction kinetics. We focus on the impact of the mixing degree between chemical species and its role in the global reaction behavior. We first consider a reactive displacement in a Poiseuille flow through a pore channel, this system allow us to quantify the impact of the interaction of interface deformation and diffusion on mixing and reactive transport. We observe overestimation of the global reaction efficiency by the use of the Taylor dispersion coefficient at preasymptotic times, when the system is characterized by incomplete mixing. Next, we observe features of incomplete mixing in a synthetic porous medium. Results show that macroscopic predictions using the hydrodynamic dispersion coefficient overestimates the amount of reaction. In addition, we analize the bimolecular reactive transport in a laboratory experiment, where we find that the amount of reaction is affected by the amount of mixing due to difusion, the amount of mixing due to spreading and the degree of heterogeneity of the flow field. The contributions of these factors induces that ADRE estimation of the total reaction product fails. In order to characterize incomplete mixing and provide an explicit relation between fluid deformation and its impact on the temporal evolution of the chemical reactivity, we develop the dispersive lamella approach based on the concept of effective dispersion which accurately predicts the full evolution of the product mass. Specifically, the approach captures the impact of interface deformation and diffusive coalescence. Using this methodology, we quantify the impact of flow heterogeneities on the amount of fluid mixing in a pore channel, where we observe three temporal regimes based on the production rate of the product mass. In addition, the dispersive lamella predictions capture the kinetics of the reaction in a synthetic porous medium. Results reveal that reaction behavior is controlled by the interface front between the two reactants. In the pore-scale experimental visualization, the dispersive lamella show that reaction is controlled by the deformed mixing interface at early times, and for fingering coalescence at late times.Los modelos de transporte reactivo son una herramienta importante para el análisis de procesos físicos y químicos en los sistemas terrestres. Los procesos de transporte reactivo observados en medios porosos heterogéneos muestran un comportamiento diferente al de las leyes de transporte para medios homogéneos. Los acuíferos exhiben heterogeneidades a todas las escalas, lo que lleva a dinámicas de transporte y reacción que no pueden explicarse mediante modelos de transporte reactivo tradicionales basados en la ecuación advocación-dispersión-reacción (ADRE). La discrepancia de este comportamiento se remonta a la naturaleza no uniforme de los campos de velocidad de flujo, a complejas distribuciones de concentración y al grado de mezcla entre los reactivos. La contribución de estos factores es clave para proporcionar predicciones precisas de las reacciones químicas. Por lo tanto, la caracterización completa de las reacciones químicas requiere que los modelos determinen los mecanismos básicos que gobiernan la dinámica de mezcla y reacción. En esta tesis, presentamos una metodología para la simulación de reacciones químicas. La metodología propuesta es un “random walk particle tracking” (RWPT) acoplado a reacciones que simula reacciones químicas bimoleculares, y es equivalente a la ADRE. Las reacciones entre partículas están determinadas por una probabilidad de reacción basada en el coeficiente de velocidad de reacción, el número total de partículas y el radio de interacción que describe un volumen de mezcla completa en el que todas las partículas tienen la misma probabilidad de reaccionar. El RWPT se valida frente a soluciones analíticas para diferentes escenarios de flujo con cinéticas lentas y rápidas. Además, estudiamos el impacto del grado de mezcla entre las diferentes especies químicas y su papel en el comportamiento global de la reacción. Primero consideramos un desplazamiento reactivo en un flujo de Poiseuille a través de un canal de poro. Y observamos la sobreestimación de la eficiencia global de reacción mediante el uso del coeficiente de dispersión de Taylor en tiempos preasintoticos. Observamos el grado de mezcla de los reactivos en un medio poroso sintético. Los resultados muestran que las predicciones macroscópicas que utilizan el coeficiente de dispersión hidrodinámica sobreestiman la cantidad de reacción. Además, analizamos el transporte reactivo en un experimento de laboratorio, donde encontramos que la cantidad de reacción se ve afectada por la cantidad de mezcla debida a la difusión, la cantidad de mezcla debida a la extensión de la interfaz y el grado de heterogeneidad del campo de flujo. La contribución de estos factores induce que la estimación de la masa total del producto de reacción por parte de la ADRE falle. Para caracterizar la mezcla incompleta y proporcionar una relación explicita entre la deformación del fluido y su impacto en la evolución temporal de la reactividad química, desarrollamos el método de la lamela dispersiva basado en el concepto de dispersión efectiva que predice con precisión la evolución de la masa total del producto de la reacción. El método capta el impacto de la deformación de la interfaz y la coalescencia difusiva. Usando esta metodología, cuantificamos el impacto de las heterogeneidades de flujo en el grado de mezcla de reactivos en un canal de poro, donde observamos tres regímenes temporales basados en la tasa de producción de la masa del producto. La predicción de las lamelas dispersivas captura la cinética de la reacción en el medio poroso sintético estudiado. Los resultados revelan que la reacción está controlada por la interfaz de mezcla entre los reactivos. En la visualización experimental a escala de poro, los resultados de las lamelas dispersivas muestran que la reacción está controlada por la interfaz de mezcla deformada en los primeros tiempos, y para la fusión de la digitación en los últimos tiempos.Postprint (published version

Trace-metaldynamics in response of increase CO₂ and iron availability in a coastal mesocosm experiment

A mesocosm experiment was performed in the Raunefjord (Norway) to study changes in dissolved Cu (dCu) and Fe (dFe), and in the elemental composition of particles during an Emiliania huxleyi dominated bloom. The CO2 treatments consisted of present (LC; 390 ppmV) and predicted levels (HC; 900 ppmV) and iron conditions were created with the addition of the siderophore desferoxamine B (DFB). Our results showed the DFB addition enhanced the solubility of Fe in this fjord environment. Initially, dFe was comparable among treatments but after the addition, the HC and/or +DFB treatments presented higher levels and finally, the only ones maintaining high dFe were the +DFB treatments. Unlike dCu presented indistinguishable levels in all mesocosms over time. Particulate metals were normalised to P and Al to evaluate the relative influence of biotic and abiotic sources. The Fe:P ratios decreased with time and compared to published phytoplankton ratios suggest Fe storage. On the other hand, Fe:Al ratios were relatively closer to the crustal ratios suggesting that the abiotic source was more important for this metal. Trends for other metals will be discussed.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

The Obligations and Regulatory Challenges of Online Broker-Dealers and Trading Platforms

(Excerpt) Investing has been evolving for decades. On “Mayday” in 1975, the SEC abolished fixed commissions, changing the face of the brokerage industry. A few months later, Charles Schwab opened its first offices, and discount brokerages were born. By the mid-1980s, there were over 600 discount brokers operating. By 1990, discount brokerage firms captured just under than 10% of the market, although Charles Schwab captured 40% of the discount brokerage market. Throughout the 1990s, new firms entered the market, including E*Trade and AmeriTrade. Online trading became more prevalent; by 1999 25% of all trades occurred online. The term “day trader” entered our vocabulary. Commissions declined, until they reached zero. Investors now have more choices than ever when deciding how and with whom to invest. In addition to the large full service brokerage firms, there are independent broker-dealers, discount brokers, and online platforms and apps. Across the models, the level of service varies, as does the minimum amount needed to open an account and the ease with which an account can be opened. Both new and experienced investors responded to these new trading models and reduced barriers to entry. 2020 witnessed a surge in new retail brokerage accounts opened on online platforms. One research analyst at JMP Securities estimates that more than 10 million new online brokerage accounts were opened in 2020. According to a joint study conducted by the FINRA Investor Education Foundation and NORC at the University of Chicago, 66% of survey respondents who opened a new account in 2020 were new investors, who had not previously owned a taxable investment account. The FINRA/NORC study found that the new investors were younger, had lower incomes, and were more racially diverse, compared to the other groups measured, specifically experienced investors that also opened online brokerage accounts in 2020, or “holdover” account owners who owned a brokerage account but did not open a new account in 2020. The FINRA/NORC study attributed the surge in new retail investors to the reduction in barriers to entry for retail investing, including no-minimum and low-minimum accounts and low or zero trading commissions. In addition to lowering the barriers to the markets, the online platforms have changed how investors interface with firms and the markets. They offer a number of different design features, commonly described as “gamification.” These may include games when an investor opens an account; animations, including confetti when a milestone is reached; social networking tools; prizes or rewards for activity streaks; points, badges, and leaderboards; lists of popular stocks; free stocks for referring additional customers; and push notifications

Technology in Legal Practice: Keeping Ethical Obligations in Mind

(Excerpt) The use of technology in the legal profession is ubiquitous, expanding, and ever changing. Lawyers connect with their clients, co-workers, and others through email. Cloud computing has allowed lawyers to create virtual and mobile workspaces, providing them with accessibility to client files and resources anywhere in the world. Social media allows lawyers to showcase their expertise and build their practice. Technology has undoubtedly impacted how lawyers provide legal services to their clients. However, as lawyers, we remain subject to long-standing professional and ethical obligations that govern our practice. This article explores how commonly used technology in legal practice implicates these ethical obligations, in particular, the duties of competence and confidentiality, and takes into account the constantly evolving guidance on these very important issues